Question 11 and 12, Exercise 6.3

Solutions of Question 11 and 12 of Exercise 6.3 of Unit 06: Permutation and Combination. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan.

Number of diagonals in n-sided polygon is 35. Find the number n?

Solution.

So given that nC2n=35orn!2!(n2)!n=35n(n1)(n2)!2(n2)!n=35n(n1)2n2=35n2n2n=70n23n70=0n2+7n10n70=0n(n+7)10(n+7)=0(n+7)(n10)=0n+7=0 or n10=0n=7n=10 n can not be negative, so n=10

For the post of 6 officers, there are 100 appliciants,
2 posts are reserved for serving candidiates and remaining for others.
There are 20 serving candidates among the appliciants. In how many ways this selection can be made?

Solution.

2 candidate would be chosen out of 20 applications of serving candidates
and 4 candidates would be chosen out of remaining 80 applicants.
Possible ways of selection
=20C2×80C4=190×1581580=300500200